"...giant sucking sound" moment

Just for grins, this was from 1992.
Prescient words from the third party guy...



What he didn't anticipate was an influx of immigrants. The "sucking sound" turns out to have been a flood of workers coming into, not out of, the country.
So here are some questions:
If unemployment is now under five percent, then who might be doing the work if several million immigrants are removed from the work force?
And what would that do to wages?
And when wages go up, what impact does that have on prices?
Am I missing something, or don't higher wages and prices drive inflation?
Just asking.